Although sequential hypothesis testing requires in general fewer samples than fixed sample size tests to reach the same error rate [1]} and could be implemented online, the framework of hypothesis testing with finite repeated observations still admits its own advantages, especially for analytical purposes. There are several large-deviation theorems such as quantum versions of Stein's lemma [2]} and Sanov's theorem [3]} characterizing that a quantum detector can achieve the exponential decay of both false alarm rate and miss rate to zero when the sample size becomes infinitely large.
